A general class of hypercube structures is presented in this paper for interconnecting a network of microcomputers in parallel and distributed environments. The interconnection is based on a mixed radix number system and the technique results in a variety of hypercube structures for a given number of processors N, depending on the desired diameter of the network. A cost optimal realization is obtained through a process of discrete optimization. The performance of such a structure is compared to that of other existing hypercube structures such as Boolean n-cube and nearest neighbor mesh computers.